An Air Carrier Captain reported a NMAC with a VFR aircraft flying just above the ceiling of Class B airspace after being climbed to a new altitude by ATC.

Narrative

Captain; me; was flying. ATC told us to level off at 7000 ft. which we did. We were on the SID level at 7000 ft. Autopilot1 was engaged. ATC told us to climb to 16;000 ft. I went to open climb and saw a target approaching us on the Navigation Display. I told First Officer look for him. Then we received a TA followed by a RA level off. Leveled off. I complied exactly to the RA. Then we did see a red fixed gear Cessna fly just in front of us; at 350 to 400 ft. above us. Then ATC issued a traffic alert to us; stop climb immediately. First Officer (FO) told ATC we received an RA and complied. ATC then told us climb to 16000 ft. I told FO your airplane my radios. I asked ATC what was that; why did you climb us to 16;000 ft ? He said he didn't see the target. I asked ATC does a VFR airplane need a clearance at 7500 ft. He said no. Either ATC errored or red Cessna transponder was off; not working; or just turned on. Per Company policy dispatch was notified. Perhaps ZZZ ATC and FAA can raise Class B to 10500 ft. from 7500 ft."